12.2.10 problem 10

Internal problem ID [1546]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:59:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {k y}{x}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

dsolve([diff(y(x),x) +k/x*y(x)=0,y(1) = 3],y(x), singsol=all)
 

\[ y = 3 x^{-k} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 12

DSolve[{D[y[x],x] +k/x*y[x]==0,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^{-k} \]